Multiply the following complex numbers: $({-3-5i}) \cdot ({-2-4i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3-5i}) \cdot ({-2-4i}) = $ $ ({-3} \cdot {-2}) + ({-3} \cdot {-4}i) + ({-5}i \cdot {-2}) + ({-5}i \cdot {-4}i) $ Then simplify the terms: $ (6) + (12i) + (10i) + (20 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 6 + (12 + 10)i + 20i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 6 + (12 + 10)i - 20 $ The result is simplified: $ (6 - 20) + (22i) = -14+22i $